Constrained Quadratic Risk Minimization via Forward and Backward Stochastic Differential Equations

In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of FBSDEs together with other conditions. We characterise explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion and vice versa. We apply the results to solve quadratic risk minimization problems with cone-constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems.Comment: 22 page

Kolmogorov Random Graphs and the Incompressibility Method

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of the maximum possible Kolmogorov complexity) and (ii) a new elementary proof for the number of unlabeled graphs.Comment: LaTeX 9 page

Recycled Glass Fiber Reinforced Polymer Composites Incorporated in Mortar for Improved Mechanical Performance

Glass fiber reinforced polymer (GFRP) recycled from retired wind turbines was implemented in mortar as a volumetric replacement of sand during the two phases of this study. In Phase I, the mechanically refined GFRP particle sizes were sieved for four size groups to find the optimum size. In Phase II, the select GFRP size group was incorporated at three different volumetric replacements of sand to identify the optimum replacement content. The mixtures were tested for compressive strength, flexural strength, toughness, and the potential for alkali-silicate reaction. Incorporation of GFRP in mortar proves promising in improving flexural strength and toughness in fiber-like shapes and 1–3% volumetric fractions

Semiparametric Estimation in Models of First-Price, Sealed-Bid Auctions with Affiliation

Within the affiliated private-values paradigm, we develop a tractable empirical model of equilibrium behaviour at first-price, sealed-bid auctions. The model is non-parametrically identified, but the rate of convergence in estimation is slow when the number of bidders is even moderately large, so we develop a semiparametric estimation strategy, focusing on the Archimedean family of copulae and implementing this framework using particular members--the Clayton, Frank, and Gumbel copulae. We apply our framework to data from low-price, sealed-bid auctions used by the Michigan Department of Transportation to procure road-resurfacing services, rejecting the hypothesis of independence and finding significant (and high) affiliation in cost signals.first-price, sealed-bid auctions, copulae, affiliation

Nanomechanical characterization of cavity growth and rupture in hydrogen-implanted single-crystal BaTiO3

A thermodynamic model of cavity nucleation and growth in ion-implanted single-crystal BaTiO3 layer is proposed, and cavity formation is related to the measured mechanical properties to better understand hydrogen implantation-induced layer transfer processes for ferroelectric thin films. The critical radius for cavity nucleation was determined experimentally from blistering experiments performed under isochronal anneal conditions and was calculated using continuum mechanical models for deformation and fracture, together with thermodynamic models. Based on thermodynamic modeling, we suggest that cavities grow toward the cracking criteria at a critical blister size whereupon gas is emitted from ruptured cavities. The main driving force for layer splitting is the reduction of the overall elastic energy stored in the implanted region during the cavity nucleation and growth as the gaseous H2 entrapped within the cavities is released. Nanoindentation measurements reveal locally the mechanical property changes within the vicinity of a single cavity. Using the measured mechanical properties at the single-cavity level, we developed three-dimensional strain and stress profiles using finite element method

Realized volatility and absolute return volatility: a comparison indicating market risk

Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models, two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.ZZ, ZQ, BL thank "Econophysics and Complex Networks" fund number R-144-000-313-133 from National University of Singapore (www.nus.sg). TT thanks Japan Society for the Promotion of Science Grant (www.jsps.go.jp/english/e-grants/) Number 25330047. HES thanks Defense Threat Reduction Agency (www.dtra.mil) (Grant HDTRA-1-10-1-0014, Grant HDTRA-1-09-1-0035) and National Science Foundation (www.nsf.gov) (Grant CMMI 1125290). ZZ thanks Chinese Academy of Sciences (english.cas.cn) Grant Number Y4FA030A01. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. (R-144-000-313-133 - National University of Singapore; 25330047 - Japan Society for the Promotion of Science Grant; HDTRA-1-10-1-0014 - Defense Threat Reduction Agency; HDTRA-1-09-1-0035 - Defense Threat Reduction Agency; CMMI 1125290 - National Science Foundation; Y4FA030A01 - Chinese Academy of Sciences)Published versio